Parametric spatial transformation models have been successfully applied to image registration tasks. In such models, the transformation of interest is parameterized by a fixed set of basis functions as for example B-splines. Each basis function is located on a fixed regular grid position among the image domain because the transformation of interest is not known in advance. As a consequence, not all basis functions will necessarily contribute to the final transformation which results in a non-compact representation of the transformation. We reformulate the pairwise registration problem as a recursive sequence of successive alignments. For each element in the sequence, a local deformation defined by its position, shape, and weight is computed by our recurrent registration neural network. The sum of all lo- cal deformations yield the final spatial alignment of both images. Formulating the registration problem in this way allows the network to detect non-aligned regions in the images and to learn how to locally refine the registration properly. In contrast to current non-sequence-based registration methods, our approach iteratively applies local spatial deformations to the images until the desired registration accuracy is achieved. We trained our network on 2D magnetic resonance images of the lung and compared our method to a standard parametric B-spline registration. The experiments show, that our method performs on par for the accuracy but yields a more compact representation of the transformation. Furthermore, we achieve a speedup of around 15 compared to the B-spline registration.